1. Suppose that the water level of a lake is 35 feet and that it is receding at a rate of 1.5 feet per day.

a. Write an equation for the water level, L, after D days.

b. In how many days will the water level be 20 feet?


2. Tina babysits after school and charges a flat fee of $3, plus $5 per hour.

a. Write an equation for the cost ,C, after H hours of babysitting.

b. What do the slope and the y-intercept represent in this problem situation?

c. How much money will Tina make if she babysits 5 hours?


3. An electrician charges $25 for a service call plus $50 per hour of service.

a. Write an equation in slope intercept for the cost ,C, after H hours of service

b. What will be the total cost for 8 hours of work?

c. If an electrician earned $225, how many hours did the repair last?

The value of the expression (x != 7) && (x <= y) is: B. true

The expression is a combination of two logical conditions joined by the logical operator "&&" which means "and". The first condition "x != 7" checks if x is not equal to 7, which is true because x is 5. The second condition "x <= y" checks if x is less than or equal to y, which is also true because x is 5 and y is 7.

Since both conditions are true, the entire expression evaluates to true. The logical operator "&&" only returns true if both the conditions are true, else it will return false.

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20 ribbons can be cut from the 3.6m length of ribbon.

1m=100 cm

lengths of ribbons 18 centimeters long can be cut from a length of 3.6 meters

number of ribbons = 360/18

=20

20 ribbons can be cut from the 3.6m length of ribbon.

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Descriptive statistics are used to summarize data in a useful and informative manner.

This type of statistics provides meaningful information about the data set by organizing and presenting it in an easily understandable format. Descriptive statistics can be used to summarize the data in the form of tables, graphs, and charts. It can also be used to provide detailed information about the data set, such as the mean, median, mode, standard deviation, and range.

Descriptive statistics can also be used to make inferences about a population. This is done by comparing the data collected from a sample to the characteristics of the population. By understanding the characteristics of the population, researchers can make accurate predictions about the behavior of the population.

Descriptive statistics can also be used to determine if the data adequately represent the population. This involves analyzing the sample size, data accuracy, and the assumptions made about the population. If the data does not accurately represent the population, then researchers have to make changes to their data collection process or revise their assumptions about the population.

Finally, descriptive statistics can be used to gather or collect data. This involves designing surveys, experiments, and other data collection methods. By using descriptive statistics to collect data, researchers can ensure that the data is valid and reliable.

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Answer:

13

Step-by-step explanation:

8, 10, 12, 14, 38, 42

12+14/2 = 13

Step-by-step explanation:

we create 2 equations with 2 variables by using the given point coordinates in both :

A×1 + B×-2 = 7

A - 2B = 7

A×1 - B×-2 = 3

A + 2B = 3

to solve we can simply add both equations to temporarily eliminate B and solve for A :

A - 2B = 7

A + 2B = 3

-------------------

2A 0 = 10

A = 10/2 = 5

now, we use one of the original equations to solve for B :

5 + 2B = 3

2B = -2

B = -2/2 = -1

A) p component passes on cost but fails on performance and appearance is equal to 0.02 and B) p(Comment passes on all three characteristics component passes on both ) is = 0.775                                                          

p=Component passes on performance.

Q=Component passes on appearance.

R=Component passes on cost.

we have, ( Component passes on both appearance and cost)

=p(Q∩R)

=0.40

P(Component passes on all three characteristics)

=p(p ∩ Q ∩ R)

=0.31

P(Component passes on performance)

p(p) =0.64

P(Components fails on all three characteristics)

=P(p ∩ Q ∩ R)

=0.06        

(a) What is the likelihood that a component saves money but fails in terms of performance and appearance?

p( P ∩ Q ∩ R)
=P(P∩Q)-P(P∩Q∩R)
=(P(P)-P(P∩Q))-0.19
=1-0.64-P(P∩Q)-0.19
=0.17-P(P∩Q)
=0.17-P(P∩Q∩R)-0.06
=0.11-P(Q∩R)-P(P∩Q∩R)
=0.11.(0.40-0.31)
=0.02


B) What is the likelihood that a component will pass on all three characteristics?
if it passes on both appearance and cost:

P(P∩Q∩R|Q∩R)          
P(P∩Q∩R|Q∩R)=P(P∩Q∩R)/P(Q∩R)
=0.31/0.40

=0.775    

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Answer:

15

Step-by-step explanation:

to find f(5), all you do is substitute 5 for both of the x's. do this in a calculator and you'll get the same thing as i did.

The value of the iterated integral after converting it to polar coordinates and solving it is 2.

What is integral ?

An integral in mathematics is either a numerical value equal to the area under the graph of a function for some interval or a new function, the derivative of which is the original function (indefinite integral).

The integral becomes ,

∫∫_D rdrdθ where D is the region in the polar coordinates.

The region D is defined by the constraints ,

0 <= r <= 2cos(θ) and 0 <= θ <= pi/4

So, the integral is ∫^(pi/4)_0∫^(2cos(θ))_0 rdrdθ = (1/2) ∫^(pi/4)_0 (2cos(θ))^2 dθ = (1/2) ∫^(pi/4)_0 4cos^2(θ) dθ

Now we can solve the integral by integration by parts,

u = 4cos^2(θ)

du/dθ = -8sin(θ)cos(θ)

dv/dθ = 1

v = θ

∫^(pi/4)_0 4cos^2(θ) dθ = [4cos^2(θ)θ]^(pi/4)_0 - ∫^(pi/4)_0 -8sin(θ)cos(θ)θ dθ

The value of the iterated integral after converting it to polar coordinates and solving it is 2.

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The pound per hour when the movie theater went through 2 pounds of popcorn every 9 hours is 2/9 pounds

Ratio in Mathematics simply demonstrates how many times one number can be able to fit into another number. It should be noted that ratios contrast two numbers by dividing them. In this case, A/B will be the formula if one is comparing one variable (A) to another variable (B).

In this case, the movie theater went through 2 pounds of popcorn every 9 hours. The pound per hour will be:

= Number of pound / Number of hours

= 2/9

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Answer:

3/4

Step-by-step explanation:

1 batch of cookies is equal to 0.375. 3/4 a barrel of cookies is equal to 0.75. 0.75/0.375 is equal to 2. So 3/4 a barrel is 2 batches of cookies.

Answer:

5-30

Step-by-step explanation:

expectation of single

The comparison of the expressions is 7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

From the question, we have the following parameters that can be used in our computation:

7 + 3^2-2x5÷4-1x2 and (¾+ ⅛) ÷ ⅛ - 2^2

Express the exponents properly

This gives

7 + 3² -2  * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 2²

Evaluate the exponents

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and (¾+ ⅛) ÷ ⅛ - 4

Evaluate the expressions in brackets

So, we have the following representation

7 + 9 - 2 * 5 ÷ 4 - 1 * 2 and 7/8 ÷ ⅛ - 4

Solve the products and quotients

7 + 9 - 2.5 - 2 and 7 - 4

So, we have

11.5 and 3

11.5 is greater than 3

So, we have

11.5 > 3

Rewrite as

7 + 3² -2  * 5 ÷ 4 - 1 * 2 > (¾+ ⅛) ÷ ⅛ - 2²

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It is possible for an exponential equation to have two different solutions. This is true.

An exponential equation is an equation in which the variable appears in an exponent. For example, an equation of the form f(x) = a^x is an exponential equation, where a is a constant and x is the variable.

In general, exponential equations can have multiple solutions. For example, the equation 2^x = 8 has two solutions, x = 3 and x = -1/3. The reason for this is that the exponential function, f(x) = a^x, is periodic, so it repeats its values after a certain interval.

In the case of exponential equations which is having a base that is greater than 1 , such as 2^x = 8, in such cases it will have two solutions as it will be increasing for all x.

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A transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6).

∠1 ≅ ∠5 (corresponding angle theorem)

∠7 ≅ ∠5 (vertical angle theorem)

∠1 ≅ ∠7 (Transitive property of congruence)

Complete question is at the end of solution.

As per the given data, a transversal line intersects two parallel lines a and b.

The values of corresponding angles congruent pairs of corresponding angles are (1, 5), (4, 8), (3, 7), and (2, 6)

Line a is parallel to line b.

Therefore,

a ║ b

Let's prove ∠1 ≅ ∠7

Hence,

∠1 ≅ ∠5 (corresponding angle theorem)

Corresponding angles are the angles that are formed in matching corners or corresponding corners with the transversal when two parallel lines are cut by the traversal.

∠7 ≅ ∠5 (vertical angle theorem)

Vertical angles theorem or vertically opposite angles theorem:

According to the theorem, two opposing vertical angles that are created when two lines cross one other are always equal.

Vertical angles are the angles formed when two lines intersect each other.

∠1 ≅ ∠7 (Transitive property of congruence)

Transitive property of congruence: If two lines, angles, or triangles are congruent with one another, then the first line, angle, or triangle is congruent with the second, third, or fourth line, angle, or triangle.

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The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

Given 2. Corresponding angles theorem 3. Vertical angles theorem 4. Transitive property of congruence Reasons: 1. The transversal line intersects two parallel lines a and b with values of corresponding angles congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). 2. If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent. 3. If two angles are vertical angles, then they are congruent. 4. If two angles are congruent to the same angle, then they are congruent to each other.

The given statement states that a transversal line intersects two parallel lines, a and b, with corresponding angle congruent pairs of (1, 5), (4, 8), (3, 7), and (2, 6). The proof uses the corresponding angles theorem, vertical angles theorem, and transitive property of congruence to show that the angles are congruent.

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Answer:

16

Step-by-step explanation:

48 divided by 3 is 16, so each of his friends will get 16 cookies.

The solution to the system of equations is (3,1).

2x - 3y = 6

3x + 2y = 7

(3,1)

Multiply the first equation by 3:

6x - 9y = 18

Add the two equations:

9x - 7y = 25

Divide both sides by 9:

x - y = 25/9

Substitute 25/9 for x in the second equation:

3(25/9) + 2y = 7

Simplify:

25 + 18y = 63

Subtract 25 from both sides:

18y = 38

Divide both sides by 18:

y = 38/18

Substitute 38/18 for y in the equation x - y = 25/9:

x - (38/18) = 25/9

Simplify:

x = (25/9) + (38/18)

Simplify:

x = 63/9

Therefore, the solution is (63/9, 38/18) or (3,1).

The solution to the system of equations is (3,1).

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The values in the ratio table are as follows:

A ratio table is just a table that shows how two different quantities relate to one another. Ratio tables are useful for understanding how two different quantities relate to one another.

Given a ratio table that has the initial ratio of 4

For the first column

Ratio = 8/2 = 4

For the second column

Ratio = x/10

Since the ratio will be the same

=> 4 = x/10

=> x = 40

For the third column

Ratio = 56/x

=> 4 = 56/x

=> x = 14

For the fourth column

Ratio = x / 18

x = Ratio *18

x = 72

Therefore, The values in the ratio table will be 40, 14, and 72

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Answer:

x = 2

Step-by-step explanation:

6/3 = 2

Answer:

Step-by-step explanation:

do it better than what you did before.

The ratio of surface area to volume for each triangular prism will be;

⇒ 224 : 2592

A ratio indicates how many times one number contain in another number. The ratio of two number is written as x : y, which is equivalent to x/y. Where, x and y are individual amount of two quantities. And, Total quantity gives after combine as x + y.

Given that;

In first figure,

The height of triangular prism = 4 cm

The base of triangular prism = 3 cm

The Length of triangular prism = 8 cm

In second figure,

The height of triangular prism = 12 cm

The base of triangular prism = 15 cm

The Length of triangular prism = 24 cm

Now,

We know that;

The volume of triangular prism = (Perimeter of base × length of prism)            

                                                    + (2 × Base area)

In first figure,

Perimeter of base = 2 (3 + 8)

                            = 22 cm

And, Area of base = 3 × 8

                           = 24 cm²

Thus, We get;

The volume of triangular prism = (Perimeter of base × length of prism)            

                                                    + (2 × Base area)

                                               = (22 × 8) + (2 × 24)

                                               = 176 + 48

                                               = 224 cm³

In second figure,

Perimeter of base = 2 (15 + 24)

                            = 78 cm

And, Area of base = 15 × 24

                           = 360 cm²

Thus, We get;

The volume of triangular prism = (Perimeter of base × length of prism)            

                                                    + (2 × Base area)

                                               = (78 × 24) + (2 × 360)

                                               = 1872 + 720

                                               = 2592 cm³

So, The ratio of surface area to volume for each triangular prism will be;

⇒ 224 : 2592

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Angle DBC and angle ADB constitute a pair of alternate internal angles which are congruent," which concludes the evidence.

The final sentence that establishes that ABCD is a parallelogram is "Angle DBC and angle ADB form a set of alternate interior angles which are congruent."

A parallelogram has opposing sides that are parallel and equal.

AB = DC and AB || DC as stated. Only AD || BC and AD=BC need to be demonstrated. As a result, the qualities of AD=BC are demonstrated. And a pair of alternative interior angles for demonstrating AD || BC should be equal.

This leads to Phrase C, "Angle DBC and angle ADB constitute a pair of alternate internal angles which are congruent," which concludes the evidence.

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Calculating the area of a triangle:

[tex]A=\frac{1}{2}bh[/tex]

1. determine base and height measurements

2. apply the formula

[tex]A=\frac{1}{2}(12m)(8m)\\[/tex]

[tex]A = 48m^2[/tex]

The maximum load that can be applied to the wire made of that kind of steel is 21195 N. The result is obtained by using the tensile strength equation.

Tensile strength is the maximum load or stress that a material can withstand without fracture when being stretched or pulled per its cross-sectional area.

The statement can be expressed as

σ = F/A

Where

The tensile strength of a certain steel wire is 3000 MN/m². The diameter of the wire is 3.0 mm. Find the maximum load that can be applied to the wire!

Let's count the cross-sectional area!

A = πr²

A = 3,14 (½d)²

A = 3,14 [½(3.0 × 10⁻³)]²

A = 3,14 (1.5 × 10⁻³ m)²

A = 3,14 (2.25 × 10⁻⁶) m²

A = 7.065 × 10⁻⁶ m²

The maximum load is the maximum value of the force acting on it.

σ = F/A

3000 MN/m² = F / 7.065 × 10⁻⁶ m²

3000 × 10⁶ N/m² = F / 7.065 × 10⁻⁶ m²

F = 3 × 10⁹ × 7.065 × 10⁻⁶  N

F = 21.195 × 10³ N

F = 21195 N

Hence, the steel wire can have the maximum load of is 21195 N.

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Answer:

14/3

Step-by-step explanation:

Flip the second fraction's numerator and denominator to get its reciprocal of 7/3. Then, you simply multiply it by 2, which equals 14/3.

The centroid is the point at which the three medians of the triangle meet, divides each median proportionally, is always inside the triangle, equidistant from each vertex, and is the center of gravity.

1. The centroid of a triangle is the point at which the three medians (the lines connecting each vertex to the midpoint of the opposite side) of the triangle meet.

2. The centroid divides each median into two segments that are proportional to the lengths of the sides of the triangle.

3. The centroid is always inside the triangle, regardless of its shape.

4. The centroid is always equidistant from each vertex of the triangle.

5. The centroid is the center of gravity of the triangle, meaning that it is the point at which the triangle would balance if it were suspended.

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The properties of centroid of the triangle is explained below.

The term triangle is defined as the polygon with three sides, three vertices and three angle in it.

Here we need to list down the properties of the centroid of the triangle.

In order to identify the properties, first we must know the defnition of centroid.

The term centroid in math is defined as the point that is presented in at 2/3 of the distance from the vertex to the mid-point of the sides.

Here we know that the centroid has the special property that, here for each median, and the distance from a vertex to the centroid is twice that of the distance from the centroid to the midpoint of the side opposite that vertex. Here we also that the three medians of a triangle divide the triangle into six regions of equal area.

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Answer:

1/5, 20 diveded by 5 is 4, 20%

Answer:

Solution is (-1,7)

Step-by-step explanation:

Graph is shown

y=2x+9 is in red

y=6-x is in blue

Hope this helps :)

Answer:

1200

Step-by-step explanation:

12 multiplied by 2 is 24.

24 divided by 2 is 12.

12 times 100 is 12 plus 2 zeros, or 1200.